Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C27⋊((C22⋊C9)⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C9 |
| unambiguous semidirect product | C27⋊((C22⋊C9)⋊C2) |
| unambiguous semidirect product | (C22⋊C9)⋊D27 |
| derived | C27×C22⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C27×C22⋊C9 | C2 |
| Frattini | C3×C9 | C3⋊S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C32 | C3⋊D9 |
| LCS | G ▷ C27×C22⋊C9 | |
| UCS | C1 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
Polycyclic presentation:
2,3^5,2^2|b^3=e,c^3=d,d^3=f,b^a=b^2e^2,c^a=c^2d^2f^2,d^a=d^2f^2,e^a=e^2,f^a=f^2,g^a=gh,g^b=h,h^b=gh165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 870);